Frequency of a Digit in the Representation of a Number and the Asymptotic Mean Value of the Digits

We study the relationship between the frequency of a ternary digit in a number and the asymptotic mean value of the digits. The conditions for the existence of the asymptotic mean of digits in a ternary number are established. We indicate an infinite everywhere dense set of numbers without frequency...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2014-08, Vol.66 (3), p.336-346
Main Authors: Klymchuk, S. O., Makarchuk, O. P., Prats’ovytyi, M. V.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Statistics
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Summary:We study the relationship between the frequency of a ternary digit in a number and the asymptotic mean value of the digits. The conditions for the existence of the asymptotic mean of digits in a ternary number are established. We indicate an infinite everywhere dense set of numbers without frequency of digits but with the asymptotic mean of the digits.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-014-0934-7